1. We develop an individuals-based model that predicts the strength of interference between foraging animals from basic elements of their behaviour. The model is based on the same principles as previous behaviour-based interference models, but extends and adds further realism to these models. One key difference is that in our model the responses of animals to competitors are not fixed, as is assumed in previous models. Instead, animals use optimal decision rules to determine responses which maximize their intake rate. 2. The general shape of interference function generated by the model is similar to that predicted by previous behaviour-based models. Interference is insignificant at low competitor densities, but steadily increases in intensity as density rises. However, comparison with the observed level of interference between oystercatchers, Haematopus ostralegus, feeding on mussels, Mytilus edulis, shows that the model's predictive power is substantially increased through the addition of optimal decision rules. When animals have a fixed response to encounters, too much interference occurs because dominant animals waste time avoiding subdominants and subdominants waste time attempting, but failing, to steal prey from dominants. When animals use optimal decision rules, only subdominants avoid, and only dominants initiate attacks. Interference is therefore reduced and is much closer to that observed. 3. The conditions under which optimal decision rules will lead to interference are described in terms of basic elements of foraging behaviour. Interference is predicted to occur when handling time and the probability of winning fights are high, and when prey encounter rate and the duration of fights are low. These parameters are used to predict successfully the presence or absence of interference in a range of shorebird-prey systems. 4. We suggest that behaviour-based interference models will need to incorporate optimal decision rules if they are to predict accurately the strength of interference observed in real predator-prey systems.